Method and System for Signal Detection Including Positioning Signals

ABSTRACT

An assisted satellite positioning system based on detecting signals from a number of satellites includes: (a) a mobile receiver; and (b) a base station communicating with the receiver over a low-power wireless communication network, the base station providing ephemeris data of a selected number of the satellites, but not all, using a compressed data format. The ephemeris data may include data concerning doppler frequency variations or elevation variations of the selected satellites over a predetermined time interval. The doppler frequency variations and the elevation variations may be represented in the compressed format by coefficients of a polynomial function of time. The polynomial function may be weighted to have lesser relative errors in larger doppler frequencies than lesser doppler frequencies, or to have lesser relative errors in lesser elevations than larger elevations. In one implementation, the low-power wireless communication network—such as a LoRa network—that has a range of at least 10 miles.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of U.S. patentapplication (“Parent Application”), Ser. No. 17/408,909, entitled“Method and System for Signal Detection Including Positioning Signals,”filed on Aug. 23, 2021, which is a divisional application of U.S. patentapplication (“Parent Application”), Ser. No. 15/991,217, entitled“Method and System for Signal Detection Including Positioning Signals,”filed on May 29, 2018. The disclosure of the Parent Application ishereby incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to signal detection. Specifically, thepresent invention relates to signal detection for positioningapplications.

2. Discussion of the Related Art

In many positioning applications, e.g., those related to the GlobalPositioning System (GPS), a signal receiver detects signals from sourcesof known locations. An estimate of the signal's time of travel betweenthe source and the receiver (“delay”) provides an estimate of thedistance between the source and the receiver. The distances are thenused to triangulate the recipient's location. In GPS, for example,spread spectrum signals from multiple GPS satellites of known positionsand motions are detected and triangulated to get the receiver'sposition. In that example, each satellite's signal embeds a 1023-bitpseudorandom code that is repeated every millisecond. (The duration ofeach bit in the signal is known as a “chip”). To detect the signal, acorrelation is computed (“integrated”) between the received signal and areplicated signal over a selected time period. Because of thesatellite's motion related to the receiver, the integration must takeaccount a shift in frequency (“doppler”) in the received signal.Detection is achieved when the integration results in a peak valueindicating that the replicated signal aligns in both time (i.e., delay)and frequency with the received signal. If the replicated signal doesnot align with the received signal, the integration results in a zerovalue.

Typically, in GPS, the delay and doppler values are arrived aftersearching through a search space of 1 millisecond in time and 8000 Hz indoppler. After the signal is first detected (“coarse acquisition”), thesignal may be tracked to provide regular updates. In tracking, thereceiver does not search the entire search space of the coarseacquisition, provided that the tracking interval is relatively short,such that the satellite's position and motion have not significantlychanged over that tracking interval. Typically, tracking may be achievedby searching over a much smaller search space surrounding the delay anddoppler values obtained in the last coarse acquisition (e.g., within ¼chip (0.25 μs) in delay and 10-100 Hz in doppler). Of course, thegreater the precision achieved in the detecting of the delay and dopplervalues, the greater the accuracy would be achieved in the positioningapplication.

Detection of a satellite signal allows one to determine the satellite'sdistance and the corresponding motion relative to the receiver (e.g.,the acceleration towards or away from the receiver). To triangulate thereceiver's location, one needs also the absolute positions and motionsof four or more satellites. This information may be determined from the“ephemeris” information which is also transmitted in the satellitesignal. Ephemeris information is also useful for coarse acquisition at a“cold start.” (That is, coarse acquisition without any reliable a prioriinformation regarding receiver position.) A full set of ephemerisinformation covering all satellites in GPS over a period of months isabout a few 10 Kbytes long. To obtain ephemeris information from thesatellite signal, one needs to track a satellite signal for 30 secondsor more. Alternatively, the ephemeris information may be obtained over ahigh-bandwidth cellular or a wide-area network from an on-line source,such as an assisted GPS (AGPS) service.

Both satellite signal tracking and data communication may be undesirablypower-intensive for a mobile device operating from battery power. Thus,it is long desired to have energy-efficient hardware and methods forpositioning in a mobile device.

SUMMARY

According to one embodiment of the present invention, a signalprocessing device for detecting a spread spectrum signal modulated witha pseudorandom code of a predetermined number of chips, includes: (a) atemperature-compensated crystal oscillator providing a timing signalaccurate to a predetermined fraction of one of the chips; (b) a clockgenerator receiving the timing signal to generate a digital clock signalof a predetermined frequency; (c) an analog signal processing circuitreceiving the timing signal, the digital clock signal and the spreadspectrum signal and providing digital baseband samples of the spreadspectrum signal at each period of the digital clock signal; (d) acounter circuit receiving the digital clock signal to provide a timingpulse of a predetermined duration; (e) a data buffer; (f) an inputinterface circuit for the data buffer, receiving the digital basebandsamples, the digital clock signal and the timing pulse, and storing intothe digital baseband samples into the data buffer over the predeterminedduration; and (g) a processor which retrieves the stored basebandsamples from the data buffer to perform signal detection. The inputinterface circuit may be implemented by parallel-connected serialperipheral interface (SPI) circuits. The predetermined frequency of thedigital clock signal may be, for example, 16 MHz and be accurate to 1/16μs. The digital baseband samples may be samples of in-phase andquadrature channels of the baseband signal derived from the receivedspread spectrum signal.

According to one embodiment of the present invention, the analogprocessing circuit need not be powered outside of the predeterminedduration of the timing pulse. Similarly, the processor may enter a sleepstate upon completion of the signal detection. Further, the processor,the data buffer and the input interface circuit are elements of anembedded microcontroller integrated circuit.

According to one embodiment of the present invention, the signalprocessing device may be solar-powered. The signal processing device maybe provided a housing in which the temperature-compensated crystaloscillator, the clock generator, the analog signal processing circuit,the counter, the input interface circuit, the data buffer and theprocessor are mounted. In addition, the housing may include a battery, apower-regulation circuit for the battery and a solar panel convertingsolar energy into energy in the battery under control of thepower-regulation circuit. In that implementation, the solar panel may bemounted on an outside surface of the housing.

According to one embodiment of the present invention, a method fordetecting a signal, includes (a) receiving the signal; (b) computing,for each of a plurality of delay values, a correlation value between thereceived signal and a replica of the signal delayed by the delay value;(c) from the correlation values, selecting a first group of correlationvalues having non-zero values and a second group of correlation values,wherein the correlation values in the first group are increasing withincreasing delay values, and wherein the correlation values in thesecond group are decreasing with increasing delay values; and (d)estimating a delay value based on extrapolation from each of the firstcorrelation values. One implementation of estimating the delay value isbased on fitting the correlation values in the first and second group toone or more polynomials of the delay. The delay value may be estimated,for example, based on an intersection of a straight line derived fromthe first group of correlation values and a straight line derived fromthe second group of correlation values.

According to one embodiment of the present invention, an assistedsatellite positioning system based on detecting signals from a number ofsatellites includes: (a) a mobile receiver; and (b) a base stationcommunicating with the receiver over a low-power wireless communicationnetwork, the base station providing ephemeris data of a selected numberof the satellites, but not all, using a compressed data format. Theephemeris data may include data concerning doppler frequency variationsor elevation variations of the selected satellites over a predeterminedtime interval. The doppler frequency variations and the elevationvariations may be represented in the compressed format by coefficientsof a polynomial function of time. The polynomial function may beweighted to have lesser relative errors in larger doppler frequenciesthan lesser doppler frequencies, or to have lesser relative errors inlesser elevations than larger elevations. In one implementation, thelow-power wireless communication network—such as a LoRa network—that hasa range of at least 10 miles.

The present invention is better understood upon consideration of thedetailed description below, in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows signal detection system 100, in accordance with oneembodiment of the present invention.

FIG. 2 shows timing of 4-bit data signal 117 of FIG. 1 at the outputterminal of SPI circuit 104.

FIG. 3 shows matched filter output values at delays d₁, d₂, d₃, and d₄during the detection of one satellite signal.

FIG. 4 shows system 400 in which ephemeris data for positioning issupplied without a conventional data connection, in accordance with oneembodiment of the present invention.

FIG. 5 a is an exemplary estimated variation in doppler values over anext period of 120 minutes for a given satellite visible or near-visiblefrom station 302.

FIG. 5 b is an exemplary estimated variation in elevation over a nextperiod of 120 minutes for a given satellite visible or near-visible fromstation 302.

FIGS. 6 a, 6 b and 6 c shows the top, bottom and side views of hexagonalhousing 600 suitable for housing a positioning device, in accordancewith one embodiment of the present invention.

FIG. 6 d shows, provided within housing 600, printed circuit board 620,on which various circuit components may be mounted, in accordance withone embodiment of the present invention.

To facilitate cross-referencing among the figures, like elements areprovided like reference numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present inventor has developed a hardware solution which may beused, for example, in conjunction with an energy-efficient signaldetection algorithm to allow a tracking interval in a satellitepositioning application to exceed one second. One example of anenergy-efficient signal detection algorithm is disclosed in the presentinventor's U.S. patent application, Ser. No. 14/826,128, entitled“System and Method of Time of Flight Detection,” filed Aug. 13, 2015,now U.S. Pat. No. 9,439,040 (the “'040 patent”). Because of the longtracking interval, the receiver requires much less power than receiversof the prior art.

FIG. 1 shows signal detection system 100, in accordance with oneembodiment of the present invention. As shown in FIG. 1 , signaldetection system 100 includes antenna 108 for receiving a satellitesignal, low-noise amplifier 107 for amplification of the receivedsatellite signal, surface acoustic wave (SAW) filter 106 forband-limiting the received satellite signal and radio-frequency (RF)front-end processing unit 111 for demodulating and further analogprocessing of the received satellite signal. RF front-end processingunit 111 also receives oscillator signal 112 fromtemperature-compensated crystal oscillator (“TCXO”) 101. Timing signal112 also allows generating clock signal 118 in clock generation circuit102. Clock generation circuit 102 is optional in some embodiments wherecounter can receive the TCXO signal directly. According to oneembodiment of the present invention, for a GPS application, clock signal118 may be made accurate to 1/16 of a microsecond (i.e., at 16 MHz,accurate to 1/16 μs). An advantage of using oscillator signal 112 fromTXCO 101 for analog signal processing and clock signal 118 for timing isthat these signals are accurate in time independent of any change intemperature in the environment. RF front-end processing unit 111includes an analog-to-digital converter which, in accordance withconventional signal processing protocols, may provide 4-bit data signal117 per clock period of clock signal 113. Clock signals 113 and 118,which are preferably based on the same clock source (e.g., TCXO 101),may have difference frequencies. In one embodiment, clock signal 113 maybe at about 32 MHz and 118 may be at 16 MHz. The relative phase betweenclock signals 113 and 118 may be arbitrary, since the delay caused byclock generation circuit 102 and TXCO 101 may be different. In oneembodiment, 4-bit data signal 117 contains two channels providingdigital in-phase (I) and quadrature (Q) baseband samples of the receivedsatellite signal.

4-bit data signal 117 is received into a buffer in memory circuit 109,which is subsequently retrieved by central processing unit (CPU) 110 forprocessing. CPU 110 may perform the signal processing using, forexample, the energy-efficient algorithm disclosed in the '040 patent. Inone embodiment, CPU 110 may be an application-specific integrationcircuit (ASIC). In one embodiment, when a pre-determined amount of datafrom 4-bit data signal 117 is received (e.g., when the buffer in memorycircuit 109 is filled, or after a predetermined interval, such as a fewmilliseconds), an interrupt is raised to indicate to CPU 110 that datais ready for processing. For energy-efficiency, data processing in RFfront-end processing unit 111 may be switched off after the buffer inmemory circuit 109 is filled. CPU 110 may also enter a sleep mode afterprocessing the data in the buffer of memory circuit 109. Accurate timingin sampling the received satellite signal allows an extended trackinginterval (e.g., 1 second). This accurate timing is provided by TCXO 101.

In signal detection 100, counter 119 is provided to generate timingsignal 116 based on clock signal 118. As a result, timing signal 116 maybe used to mark the beginning of each tracking interval accurate toclock signal 118 (e.g., 1/16 μs). A 1-bit data buffer, which may beimplemented by a serial peripheral interface (SPI) circuit 103, providesenable signal 115 for an input interface to receive 4-bit data signal117 into the buffer circuit of memory circuit 109. Enable signal 115 isthe output value of SPI circuit 103, which is supplied by a logic value‘1’ stored in the 1-bit data buffer. When the output data of SPI circuit103 is enabled by timing signal 116, enable signal 119 transitions fromlogic value ‘0’ to logic value ‘1’ at the next falling edge of clocksignal 113. This input interface may be implemented also by fourparallel SPI circuits, indicated by reference numeral 104. In thismanner, SPI circuit 103 aligns an edge of enable signal 115 with clocksignal 113 (i.e., SPI circuit 104 samples 4-bit data signal at thefalling edge of clock signal 113). Aligning the edge of enable signal115 with clock signal 113 also helps to keep the samples of the 4-bitdata signal synchronized with each other—i.e., avoid relative bit shiftsamong them. This is particularly important when SPI circuit 104 isimplemented using four separated 1-bit SPI circuits in parallel.

In one embodiment, an embedded controller integrated circuit LPC54114,available from NXP semiconductor may be used to implement SPI circuits103 and 104, memory circuit 109, counter 119 and CPU 110. The LPC54114embedded controller includes an ARM microprocessor, an on-board memorycircuit, and 8 on-board SPI interface circuits that can be used toimplement CPU 110, memory circuit 109 and SPI circuit 103, counter 119and SPI circuit 104. In one preferred embodiment, counter 119 isimplemented so that generating timing signal 116 is not controlled by aCPU interrupt, so that the timing can be accurately controlled.

FIG. 2 shows the timing of 4-bit data signal 117 at the output terminalof SPI circuit 104. FIG. 2 shows (i) enable signal EN (i.e., enablesignal 115 of FIG. 1 ) at SPI circuit 104, (ii) data signal D (i.e.,4-bit data signal 117 of FIG. 1 ), and (iii) clock signal CLK (i.e.,clock signal 113). As shown in FIG. 2 , at time to, enable signal EN isasserted, which enables SPI circuit 104 to begin to fill the buffer inmemory circuit 109 using, for example, a direct memory access (DMA)mechanism. Following assertion of enable signal EN, at time t₁ and everyclock period of clock signal CLK thereafter, data signal D outputs 4-bitof I or Q samples from SPI circuit 104 to the data buffer in memorycircuit 109. The data is provided for a predetermined time period (e.g.,1 millisecond for 1023 chips). For example, at time t₁₀₂₃, enable signalEN is deasserted and I and Q data samples output from data signal D alsoceases.

CPU 110 may then initiate a search algorithm on the data in the databuffer, such as that taught in the '040 patent mentioned above, todetermine the delay time and doppler frequency in the satellite signalreceived. Typically, a portion of the search algorithm (known as a“matched filter”) computes a correlation between a replicated signal andthe satellite signal for a selected set of delay and doppler value pairsin the search space. FIG. 3 shows matched filter output values(correlation values) at delays d₁, d₂, d₃, and d₄ during the detectionof one satellite signal. In one embodiment, 32 delay values may be used.When the replicated signal is perfectly aligned in both delay anddoppler values with the satellite signal received, the output value ofthe matched filter is expected to be at its maximum. For somedelay-doppler value pair near the delay-doppler value pair providing themaximum, the matched filter output is non-zero, but not maximum. Inother words, assuming the doppler values are aligned, matched filteroutput values at delays d₁, d₂, d₃, and d₄ are close to but not thedelay value that provides the maximum. The delay value d_(t) thatprovides the maximum is expected to be between delays d₂ and d₃.According to one embodiment of the present invention, delay value d_(t)may be estimated from estimating the rates of change (“slopes”) of theincreasing and decreasing matched filter output values prior to andsubsequent to time d_(t), using the matched filter output values atdelays d₁ and d₂, and d₃ and d₄, respectively. With the four delays d₁,d₂, d₃, and d₄ in FIG. 4 , for example, delay d_(t) may be estimatedfrom the intersection of the straight lines joining the matched filteroutput values of delays d₁ and d₂ and the straight line joining thematched filter output values of delays d₃, and d₄. Other forms ofestimating delay d_(t) are possible, such as by fitting the increasingmatched filter output values and the decreasing matched filter outputvalues into one or more polynomials of the delay values. Another methodfor determining time d_(t) calculates a derivative (i.e., rate ofchange) of the match filter output value and estimates the time when thederivative reaches zero.

To determine the position of a receiver requires a triangulation processthat uses ephemeris information of the satellites. Further, ephemerisinformation is particularly helpful for coarse acquisition during a coldstart. Such ephemeris information may be extracted by decoding thesatellite signal received, which is a time-consuming process, orreceived from a source that is in possession of the information.Typically, accessing such a source requires a data connection over acellular telephone system or an access to the internet (e.g., WiFi oranother broadband medium). For a mobile device, such a data connectionmay not be available at any given time. In any event, communication oversuch a data connection power-consuming. The present invention provides amethod and a system that does not require the conventional dataconnection.

FIG. 4 shows system 400 in which ephemeris data for positioning issupplied without a conventional data connection, in accordance with oneembodiment of the present invention. As shown in FIG. 4 , system 400includes receiver 301 which requests ephemeris information from station302 over a low-power, long-range wireless data connection. Such alow-power, long-range wireless data connection is available from any ofa number of low power wide-area networks (“LPWAN”). One example of suchan LPWAN is the LoRa network, which provides a data connection with adata rate of about 50 bytes/second, over a range of about 30 miles.Using a data connection on the LoRa network, receiver 301 may receiveephemeris data from station 302, which may be 30 miles away. As the fullephemeris information is about 100 Kbytes, and as the data rate on theLPWAN is relatively low (e.g., 50 bytes per second), the presentinvention provides, in a compressed data format to receiver 301, onlythat portion of the ephemeris data that is essential to perform thesignal processing task at hand. In one embodiment, as the range of theLoRa communication is less than 100 miles, station 302 provides only theephemeris data that is valid a short time in the immediate future, andonly for satellites that are above its horizon (“visible”) or just belowits horizon (“near visible”).

According to one embodiment of the present invention, the ephemeris dataprovided from station 302 includes the expected doppler and the expectedelevation of each visible or near-visible satellite visible in thevicinity of station 302 within a predetermined short time period (e.g.,2 hours). FIG. 5 a is an exemplary estimated variation in doppler valuesover a next period of 120 minutes for a given satellite visible ornear-visible from station 302. To provide this estimated variation indoppler values, station 302 fits the estimated variation in dopplerfrequency to a third or fourth order polynomial and extracts thecorresponding coefficients. The algorithm for the curve-fitting givesgreater weights (i.e., minimizes the error) to the larger dopplervariation values. In one embodiment, station 302 sends, for each visibleor near-visible satellite, an identifier for the satellite, a currentdelay estimate, a current doppler estimate and the coefficients of thefitted polynomial for the doppler frequency variation. These valuesallow receiver 301 to reconstruct the doppler variation polynomialobtained from the curve-fitting process described above.

FIG. 5 b is an exemplary estimated variation in elevation over a periodof 120 minutes for a given satellite visible or near-visible fromstation 302. To provide this estimated variation in elevation values, asin the doppler variation of FIG. 5 a, station 302 fits the estimatedvariation in elevation to a third or fourth order polynomial andextracts the corresponding coefficients. Unlike the case of dopplerfrequency, the algorithm for the curve-fitting in elevation givesgreater weight (i.e., minimizes the error) to the lesser elevationvalues (e.g., −5° to 5°, or just above or below the horizon). In oneembodiment, station 302 sends, for each visible or near-visiblesatellite, a current estimate for the elevation and the coefficients ofthe fitted polynomial for the variation in elevation. These valuesenable receiver 301 to reconstruct the elevation variation polynomial.

The number of bits that are used to represent each of the coefficientsin a polynomial is minimized when the error in the fitted polynomial isallowed within certain predetermined error bars. In one implementation,for example, the error bar for the doppler frequency is ±100 Hz and theerror bar for elevation is about ±2 degrees when the elevation is atabout 15 degrees.

By sending only the ephemeris data for the visible or near-visiblesatellites and in the compressed data format, the essential ephemerisinformation may be sent to receiver 301 in the vicinity of station 302using only 100 bytes or so. Even with the low data rate in a LoRacommunication network, the ephemeris information can be provided to therequesting receiver in a few seconds. Therefore, the present inventionallows a receiver, using the compressed ephemeris data transmitted overa LPWAN, to achieve a rapid coarse acquisition.

Upon receiving the compressed ephemeris, a receiver performs acquisitionand tracking on visible satellites to calculate a pseudo-range from eachsatellite. The pseudo-ranges may be sent back to station 302 (or a AGPSserver), where the position and time of the receiver may be refinedusing the full ephemeris.

In the acquisition step, the receiver searches coarse delay and dopplervalue ranges in the delay-doppler space. The compressed ephemeris of thepresent invention helps to reduce both the number of satellites and thedoppler ranges that need to be searched during the acquisition process.The acquisition step also reduces the search space for the trackingstep. In one embodiment, the search range during tracking is about 0.5micro seconds in delay and about 100 Hz for doppler. Counter 119accurately controls the interval between acquisition and tracking, andthe intervals between successive tracking steps. The error in eachinterval is controlled to be less than the delay search range in thetracking step (e.g., in one embodiment, about ½ chip or 0.5 microseconds). According to one embodiment of the present invention, after anacquisition or a tracking step, the next delay value t_(nd) (i.e., thecenter of the next search range for the delay value) may be predictedfrom the current measured delay value t_(cd) using:

$t_{nd} = {{\frac{\Delta f}{f} \times \tau} + t_{cd}}$

where Δf is the current measured doppler value, f is the frequency ofthe signal from the satellite being tracked, and τ is the trackinginterval.

After delay t_(d) is measured for each satellite, the position of thereceiver can be determined using AGPS methods. In one embodiment, thetransmit times of at the edge of the 1-ms boundaries are not measuredand delays from 5 or more satellites are used to calculate the positionand time of the receiver. One method for such a method may be founddiscussed in “A-GPS: Assisted GPS, GNSS, and SBAS” ISBN-10: 1596933747.

In one embodiment, the sampling frequencies of RF frontend 111 aredifferent for the acquisition and the tracking steps. In the acquisitionstep, RF frontend 111 uses a lower sampling frequency (e.g., 4 MHz) toreduce the amount of calculation for the acquisition step. In thetracking step, however, the RF frontend 111 uses a higher samplingfrequency, which improves the accuracy in the delay estimate andtherefore the accuracy of the pseudo-range estimate.

According to one embodiment of the present invention, using signaldetection methods disclosed herein and in the '404 patent, the presentinvention provides a positioning device that is very low-power. In fact,such a positioning device is so low-power as can be solar-powered. FIGS.6 a, 6 b and 6 c shows the top, bottom and side views of hexagonalhousing 600 suitable for housing such a positioning device, inaccordance with one embodiment of the present invention. Housing 600 ofFIGS. 6 a, 6 b and 6 c may be 2-inch long along each hexagonal side andabout ½ inch thick. As shown in FIG. 6 a, solar panel 1 may be mountedon the top cover of housing 600. Communication antenna 2, forcommunication over a LPWAN (e.g., a LoRa network), may be mounted alongone side of hexagonal housing 600.

FIG. 6 d shows, provided within housing 600, printed circuit board 620,on which various circuit components may be mounted, in accordance withone embodiment of the present invention. Printed circuit board 620includes (i) GPS antenna 3, for receiving the satellite signals forsignal detection, (ii) communication module 4, coupled to communicationantenna 2, for transmitting and receiving data signals over the LPWAN(e.g., a LoRa network), (iii) positioning module 5, which includes thecircuits shown in FIG. 1 , (iv) rechargeable battery 8 (e.g., a batterybased on lithium chemistry), (v) power module 7, coupled to both solarpanel 1 and battery 8, configured to regulate power regulationoperations, e.g., charging battery 8, and (vi) control module 8, whichgenerally controls the circuits mounted on printed circuit board 620.

The above detailed description is provided to illustrate specificembodiments of the present invention and is not intended to be limiting.Numerous modifications and variations within the scope of the presentinvention are possible. The present invention is set forth in theaccompanying claims.

I claim:
 1. A method for detecting a signal, comprising: receiving thesignal; computing, for each of a plurality of delay values, acorrelation value between the received signal and a replica of thesignal delayed by the delay value; from the correlation values,selecting a first group of correlation values having non-zero values anda second group of correlation values, wherein the correlation values inthe first group are increasing with increasing delay values, and whereinthe correlation values in the second group are decreasing withincreasing delay values; and estimating a delay value based onextrapolation from each of the first correlation values.
 2. The methodof claim 1, wherein estimating the delay value is based on fitting thecorrelation values in the first and second group to one or morepolynomials of the delay.
 3. The method of claim 2, wherein estimatingthe delay value is based on an intersection of a straight line derivedfrom the first group of correlation values and a straight line derivedfrom the second group of correlation values.
 4. A method for tracking asatellite, comprising: determining a current delay value and a currentdoppler value based performing a acquisition or a tracking step; andafter a predetermined time interval, searching for the next delay valueand the next doppler value using a delay search range centered at thesum of current delay value and the product of the predetermined timeinterval and a ratio between the current doppler value and the satellitesignal frequency.